• What are Harmonics?


    ● The presence of harmonics in electrical systems means that current and voltage are distorted and deviate from sinusoidal waveforms.


    examples of distorted current waveform

    Concept and causes of Harmonics


    ● Harmonic currents are caused by non-linear loads connected to the distribution system.

    ● A load is said to be non-linear when the current it draws does not have the same waveform as the supply voltage.

    ● Variable speed motors and drives, photocopiers, personal computers, laser printers, fax machines and battery chargers are examples of non-linear loads

    ● The flow of harmonic currents through system impedances in turn creates voltage harmonics, which distort the supply voltage.

    ● Harmonics increase power system heat losses and power bills of end-users

  • Fourier series analysis of harmonics


    The Fourier theorem states that all non-sinusoidal periodic functions can be represented as the sum of terms (i.e. a series) as follows:

    graphic representation of non-sinusoidal periodic functions

    The harmonic of order h (commonly referred to as simply the hth harmonic) in a signal is the sinusoidal component with a frequency that is h times the fundamental frequency.


    mathematical equation

    • DC component V0 = 0 (since positive area=negative area)
    • Only odd order harmonics for square wave (since odd function)
    • No even order harmonics V2 = V4 = V6 = V8 ..... = 0 (since odd function)


    Activity

    Open the interactive Excel file on GCU Learn titled:
    Harmonics.xls
    Use the interactive file to build a square wave (as in slide 5) using odd harmonics only (as in the Fourier series equation) up to the 9th harmonic.

    table of harmonic information

    The figure shows an example of a current wave affected by harmonic distortion on a 50Hz electrical distribution system. The distorted signal is the sum of a number of superimposed harmonics:

    harmonics graphs

    • The value of the fundamental frequency (or first order harmonic) is 50 Hz,

    • The 3rd order harmonic has a frequency of 150 Hz,

    • The 5th order harmonic has a frequency of 250 Hz,

    • etc ....









    Calculations using harmonics


    Total power generated by a harmonic signal is due to sum of powers at each harmonic:

    maths equation of harmonic signal power generation

    The RMS voltage of the harmonic signal is achieved by the sum of square individual harmonic RMS voltages:

    math equation of harmonic signal voltage

    The individual harmonic distortion factor:

    equation of an individual harmonic distortion factor

    Total Harmonic Distortion


    The Total Harmonic Distortion (THD) is an indicator of the distortion of a signal. It is widely used in electrical engineering and Harmonic management in particular. The THD is defined as:

    total harmonic sidtortion factor equation

    THD is the ratio of the RMS value of all the harmonic components of the signal, to the fundamental.

    Note that THD can exceed 1 and is generally expressed as a percentage.


    line and wave graph representation of THD

  • Load and supply harmonics


    • Rectifier dc voltage contains harmonics
    • Lowest order is p (pulse number)
    • Harmonics of np also exist
    • Controlled rectifier has higher harmonics content vs. uncontrolled


    graphic of load and supply harmonics

    Load harmonic voltage leads to harmonic current
    Level current is not always justified as there is no infinite inductance
    Ripple in load,
    Even harmonics, (n * 50 Hz), n=2,4,…



    harmonic voltage graph

    ● At the supply side:
    ● Sinusoidal voltage with power flow to load
    ● Non-sinusoidal current will be drawn
       - load transmits harmonic power back to supply
       - Load is harmonic generator
    ● Even harmonics are cancelled but, odd harmonics are existing
    ● Non-sinusoidal current will be drawn
    ● Vs voltage drop across supply impedance
    ● Vs depends on the harmonic contents
    ● Vc for other customers will be non-sinusoidal at PCC
       - Regulation of harmonics at PCC
       - Multiple- harmonics
       - Sub-harmonics (flickers)


    image showing supply, converter and load

  • Electro-magnetic interference


    ● Switching high current and voltages, generate unwanted signals,

    ● Affects other electronics systems

    ● EMI known as Radio Frequency Interference (RFI) is quite severe,
       - System acts as high frequency transmitting antenna
       - Propagate through cables
       - Low voltage gate control circuit can be affected as well

    ● Power and communication cables must be isolated

  • Electromagnetic compatibility (EMC)


    What is EMC? 

    ● A device that does not cause intolerable interference to other devices or itself (e.g. control circuit affected by switching)
    ● Is immune to disturbance from EMI



    Three methods for realization of EMC:

    ● Source of EMI – reduce source emission
    ● Media through it is transmitted- block propagation path
    ● Receptor – make it less susceptible

    Categories of disturbance

    ● Conducted via leads to supply- limited by using filters
    ● Radiated through the air as HF radiation- limited by screening, earthing, PCB layout


    International / European Standards

    ● BSI (UK), FCC (USA), VDE (Germany), EN (EU)
    ● Define legal limits (volt and frequency)

  • Control/mitigation of harmonics


    ● Harmonics can be mitigated by:

    1. Controlling generation within converter:
       - e.g. PWM to minimise low frequency harmonics
       - High frequency switching harmonics (from carrier signal) can be easily filtered with a low pass filter since they are at the high end of the spectrum

    PMV waveform and Harmonic spectrum

    2. By using filters:
       - Smoothing/filters on rectifier outputs
       - Low pass filters on inverters
       - Harmonic line traps
       - Screening

    ● We will study different types of harmonic filters:
       -Rectifier output smoothing
       -Inverter output filtering
       -AC line filter
       -Radio interference suppression

  • Types of filters


    1. Rectifier output smoothing


    Inductance only: similar to inductive load, smooths current

    Capacitance only: charging & discharging, RC time constant

    Combination: C maintains voltage, L smooths current. Higher-order harmonics are attenuated by the filter transfer function:


    math equation of rectifier output smoothing.

    2. Inverter output filtering


    quasi square wave and PMV-based wave graphics

    ● Inverter output, quasi-square, PWM
    ● Typical THD =5%

    simple low pass filter equation

    ● If inverter designed to eliminate low order, LPF adequate for higher order elimination


    3. AC line filter

    circuit diagram of ac line filter

    ● Each branch is tuned for specific harmonic order
    ● Losses at fundamental may be significant
    ● Frequency drifts from nominal must be taken into account during design, or
    ● Use auto tuned filter



    types of filters

    4. Radio Interference Suppression


    ● Switches give rise to mains-borne harmonics in RF range

    ● RFI with communication system. Originates from:
       - Switches- limited by screening
       - Load equipment- limited by screening
       - Radiation from the supply lines- limited by filter


    Example on filter design


    A single-phase 50 Hz bridge rectifier is fed at 70.71 V (rms). The load is a resistance of 200 Ohms. Design an LC filter for the purpose of providing a maximum ripple factor of 3% ( explain any assumptions made ).


    emample of filter design
    example solition example solution continued example solution final part

  • Check your understanding by answering the following:


    Explain what is meant by non-linear loads highlighting their impact in creating harmonic currents and voltages
    Show how Fourier Theorem is used to represent a non-sinusoidal periodic function.
    Briefly explain what is meant by the term “harmonic of order h”.
    Define the term “Total Harmonic Distortion”.
    Discuss the impact of using rectifiers on harmonics at supply and load sides.
    Explain what is meant by electromagnetic compatibility and state THREE methods of realizing it.
    Mention TWO categories of disturbance that EMC systems and how these disturbances can be limited
    Explain how the impact of harmonics can be mitigated in power electronic circuits. Include in your answer mention about PWM techniques to mitigate harmonics and different types of filter circuits.
    A square wave has:
    (i) Odd harmonics only
    (ii) Even harmonics only
    (iii) Odd and even harmonics
    (iv) Odd harmonics and DC component
    Select only ONE correct answer.
    Determine whether these statements are TRUE or FALSE:
    (i) Harmonics do not affect power system losses nor power bills of end-users
    (ii) Total power generated by a harmonic signal is due to sum of powers at each harmonic.
    (iii) The RMS voltage of the harmonic signal is achieved by the sum of the square individual harmonic RMS voltages
    (iv) In AC line filters, each branch is tuned for a specific harmonic order